Which quadratic equation is equivalent to (x - 4)² - (x - 4) - 6 = 0?

Solution:

Let's write the equation in it's standard form.

(x - 4)² - (x - 4) - 6 = 0

[ x² - 8x + 16 ] - x + 4 - 6 = 0

x² - 8x - x + 16 + 4 - 6 = 0

x² - 9x + 14 = 0 → [ similar to the standard form of quadratic equation ax² + bx + c = 0 ]

Thus, x² - 9x + 14 = 0 is the standard form of (x - 4)² - (x - 4) - 6 = 0.

Which quadratic equation is equivalent to (x - 4)² - (x - 4) - 6 = 0?

Summary:

(x - 4)² - (x - 4) - 6 = 0 is equivalent to x² - 9x + 14 = 0